What do we know?

Even if scientists are relatively convinced that dark matter really exists, there is still no consensus on what it is composed of. So far, astrophysical evidence can only tell us two facts about dark matter:

How much dark matter there is - roughly 20% of the universe's total mass density. This can be compared against predictions from particular models for dark matter - some theories give too much, some give too little.

Dark matter is fairly cold - that is, its particles are relatively slow-moving. If dark matter were composed of relativistic particles (e.g. neutrinos), it would not clump as well under its own gravity and would wash out certain smaller structures of galaxies in the universe, which is not what we observe.

Within these constraints there are still many possibilities for dark matter.

Weakly Interacting Massive Particles (WIMPs)

Many theories which seek to extend our current understanding of particle physics predict new particles, often with masses comparable to those of the W and Z bosons (around 100 GeV - 100 times the mass of a proton). In many cases the lightest of these new particles is stable, never decaying to lighter particles. Such particles turn out to be extremely interesting candidates to comprise the universe's dark matter.

A fraction of a second after the Big Bang the universe was so hot that new particles (and antiparticles) were created and destroyed all the time, just like in a particle accelerator. As the universe expanded and cooled these particles were no longer created, and eventually the leftovers annihilated or decayed, clearing the universe of these exotic states. A weakly-interacting particle like a neutrino, however, will not be able to completely annihilate and a residue of these particles will be left filling the universe. It turns out that a stable particle of mass near 100 GeV and interacting via the weak force (just the kind of particle that particle physicists think exists anyway) will leave just about the right amount of "leftovers" to account for the observed dark matter density! This class of natural dark matter candidates is generally called weakly interacting massive particles (WIMPs).

Specific WIMP theories include:

Supersymmetry: Perhaps the most popular extension to the Standard Model, supersymmetry predicts that each particle in the Standard Model has a heavier partner of different spin but similar interactions. The lightest of these particles (the lightest superpartner or LSP) is stable in many cases (if a symmetry called "R-parity" is exact), and is often a neutralino (one of the partners of the Z boson, photon, and Higgses) - an excellent dark matter candidate.

Extra Dimensions: Many theorists also suggest that our universe may have more spatial dimensions than the three we are familiar with. A fourth one may be curled up very small, for example, as if each point in our familiar space were actually a tiny ring which a particle could run around. Particles moving around such rings would look like more massive versions of the Standard Model particles, and the lightest of these (the lightest Kaluza-Klein particle or LKP) is often stable as well (and a good dark matter candidate).

Axions

There are other possible dark matter candidates which do not fit into the WIMP framework. The most popular such candidates are called axions and arise from attempts to explain why the strong interaction seems to obey a certain symmetry called "CP symmetry". Among other things, CP symmetry would prevent the neutron from having a large electric dipole moment - without it, it's very hard to understand why such a dipole moment has not yet been detectoed. The best explanation for this is called "Peccei-Quinn symmetry", and predicts a new light neutral particle called the axion.

The axion is stable in many theories, and can also be produced in the early universe. Though axions are far lighter than WIMPs (often 1 eV or much less), they can be created in the right amount by a non-thermal process which also naturally leaves them slow-moving.

Exotic Candidates

In addition to the mainstream candidates above, many more exotic candidates have been suggested - WIMPzillas, Q-balls, gravitinos, etc.